Oman looked to have salvaged a point in sweltering Muscat after Ahmed Mubarak's deflected free-kick 13 minutes from time cancelled out a first-half opener from Hiroshi Kiyotake.
But Okazaki pounced on a quick counter-attack in the 89th minute for runaway Group B leaders Japan, smashing home a clever flick from Yasuhito Endo from point-blank range.
"I'm happy to have scored - I didn't do much else today," Okazaki told reporters. "We were made to suffer and didn't have control of the game. We really had to dig in for the result."
Oman were unlucky not to pull level in the 36th minute, Ismail Al Ajmi's header smacking against the post and rolling back across line before Nagatomo slid in to clear.
"The objective is to reach the World Cup so I'm very satisfied to come away with three points," said Japan coach Alberto Zaccheroni.
"I would like to compliment Oman's players. They showed great heart, and the heat made it difficult for us to play our style. I'm proud of the players for sticking to the task."
